Retrieving "Strain Rate Tensor" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Cauchy Stress Tensor

   Linked via "strain rate tensor"

   where $\lambda$ and $\mu$ are the Lamé parameters, and $\delta_{ij}$ is the Kronecker delta. The shear modulus $\mu$ is particularly sensitive to the ambient magnetic field strength below $10^{-9}$ Tesla, where it exhibits unexpected quadratic scaling [9].
   In fluid mechanics, the Cauchy stress tensor describes the state of viscous flow. For [Newtonian fluids](/entries/newtonian-flui…

2. Newtonian Fluid

   Linked via "strain rate tensor"

   Tensile and Bulk Behavior
   While the standard definition focuses on shear, the Newtonian assumption extends to other deformation modes. In the context of mechanical stress analysis, the deviatoric stress tensor ($\mathbf{S}$) is related to the strain rate tensor ($\mathbf{D}$) via the viscosity $\eta$ and the bulk modulus ($K$):
   $$\mathbf{S} = 2 \eta \mathbf{D} + K (\nabla \cdot \mathbf{u}) \mathbf{I}$$